The authors consider the equation (1) \({\partial m \over \partial t} = - m + \text{tanh} \{\beta J^* m\}\), where \(m : \mathbb{R} \times \mathbb{R}_ + \to \mathbb{R}\); \(\mathbb{R} \ni \beta > 1\); \(J \in C^ 2 [-1,1]\) is a nonnegative, even function with the integral equal to 1; \((J^*m) (x) : = \int J (x - y) m(y)dy\). Results on existence, uniqueness and global stability of special stationary solutions of (1) called instantons are proved.